Thermal expansion coefficient mismatch

In the previous section it was pointed out that thermal stresses, arising from the thermal expansion coefficient mismatch between PS and PB, play a significant role in determining the rate of craze growth for the case of the cavitation mechanism. DiCorleto and Cohen made a detailed examination of the extent... 

The residual thermal stresses in a substrate-coating combination are due to the interfacial forces arising from the thermal expansion coefficient mismatch between coating and substrate and from the presence of a ending moment [1]. The former are uniformly distributed over the film thickness while the latJe - arises from the requirement to balance the external bending moment induced by the interfacial force in a coating-substrate combination and varies across the film thickness [2]. 

Thermal expansion coefficient (ai) the thermal expansion coefficient mismatch between the epoxide and a substrate may need to be minimised. 

Fig. 9. Residual stresses owing to thermal expansion mismatch between a particle with radius a and thermal expansion coefficient and a matrix with thermal expansion coefficient The stresses illustrated here are for and P is the interfacial pressure.

Cathodoluminescence microscopy and spectroscopy techniques are powerful tools for analyzing the spatial uniformity of stresses in mismatched heterostructures, such as GaAs/Si and GaAs/InP. The stresses in such systems are due to the difference in thermal expansion coefficients between the epitaxial layer and the substrate. The presence of stress in the epitaxial layer leads to the modification of the band structure, and thus affects its electronic properties it also can cause the migration of dislocations, which may lead to the degradation of optoelectronic devices based on such mismatched heterostructures. This application employs low-temperature (preferably liquid-helium) CL microscopy and spectroscopy in conjunction with the known behavior of the optical transitions in the presence of stress to analyze the spatial uniformity of stress in GaAs epitaxial layers. This analysis can reveal,... 

Cyclic Oxidation In many industrial applications it is particularly important for the component to be resistant to thermal shock for example, resistance-heating wires or blading for gas turbines. Chromia, and especially alumina, scales that form on nickel-base alloys are prone to spalling when thermally cycled as a result of the stress build-up arising from the mismatch in the thermal expansion coefficients of the oxide and the alloy as well as that derived from the growth process. A very useful compilation of data on the cyclic oxidation of about 40 superalloys in the temperature range 1 000-1 I50°C has been made by Barrett et... 

The crystal quality of the InGaN QWs becomes poor mainly due to the lattice-constant mismatch and the difference of the thermal expansion coefficient between InN and GaN with increasing the In composition [4,5]. Therefore, in order to improve the external quantum efficiency (i/ext) of the InGaN-based LEDs and LDs, it is important to elucidate and optimize the effects of the various growth conditions for the InGaN active layer on the structural and optical properties. Recently, we reported a fabrication of efficient blue LEDs with InGaN/GaN triangular shaped QWs and obtained a substantial improvement of electrical and optical properties of the devices [6,7]. 

The membrane layout should be as symmetric as possible to achieve good temperature homogeneity over the membrane area and, as a consequence, low stress gradients. This includes also thermal stress owing to the mismatch of the thermal expansion coefficients of the layer materials. 

The successful operation of SOFCs requires individual cell components that are thermally compatible so that stable interfaces are established at 1000°C (1832°F), i.e., thermal expansion coefficients for cell components must be closely matched to reduce stresses arising from differential thermal expansion between components. Fortunately, the electrolyte, interconnection, and cathode listed in Table 8-1 have reasonably close thermal expansion coefficients [i.e., 10 cm/cm°C from room temperature to 1000°C (1832°F)]. An anode made of 100 mol% nickel would have excellent electrical conductivity. However, the thermal expansion coefficient of 100 mol% nickel would be 50% greater than the ceramic electrolyte, or the cathode tube, which causes a thermal mismatch. This thermal mismatch has been resolved by mixing ceramic powders with Ni or NiO. The trade-off of the amount of Ni (to achieve high conductivity) and amount of ceramic (to better match the other component thermal coefficients of expansion) is Ni/YSZ 30/70, by volume (1). 

Approaches to resolving the mismatch caused by different component materials thermal expansion coefficient include increasing the fracture toughness of the electrolyte, controlling the electrolyte processing faults, varying the component thickness, and adding minor constituents to alter the anode properties. 

Contours of maximum principal stress in the first slice (near the gas inlets) and the sixth slice (near the gas outlet) are shown in Figures 5.11 and 5.12 respectively. It can be seen that the stack is partially under compression and partially under tension due to the mismatch in the thermal expansion coefficient of the materials and non-uniform temperature. In each cross-section, the stresses are higher near the top of the stack than near the bottom. Also, the stresses are higher near the gas outlet than near the gas inlets. Maximum tensile and compressive stresses in all the slices are found to be 60 MPa and 57.2 MPa respectively which are in the electrolyte layer of the last slice. The maximum stresses in all the layers are found to be well within the failure limits of their respective materials and hence thermal stress failure is not predicted for this stack. 

A thermally induced residual stress. The origin of the residual stresses is a mismatch of thermal expansion behaviors among the components. Rigid connection of each component with different thermal expansion coefficients causes residual stresses. For example, the electrolyte and electrodes are fabricated and connected at a high temperature. If the thermal expansion behaviors are not identical among the components, residual stresses will occur in the cell at room temperature. For stacks, similar residual stresses will occur by a mismatch of thermal expansion behavior among cells and other stack components. 

For most particulate composites the mismatch between the particles and the matrix is more important than the anisotropy of either component (though alumina/aluminium titanate composites provide a notable exception and are described below). The main features of the stresses can therefore be understood in terms of a simple elastic model assuming thermoelastic isotropy and consisting of a spherical particle in a concentric spherical shell of matrix with dimensions chosen to give the appropriate volume fractions. The particles are predicted to be under a uniform hydrostatic stress, ap after cooling. If the particles have a larger thermal expansion coefficient than the matrix, this stress is tensile, and vice versa. For small particle volume fractions the stress... 

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